Referring to problem 4, the operations manager at Macon Controls believes that pessimistic demand has a probability of 20 percent; expected demand has a probability of 50 percent and optimistic demand has a probability of 30 percent. Currently, new machines must be purchased at a cost of $500,000 a piece, the price charged for each control unit is $110, and the variable cost of production is $50 per unit. a. Draw a decision tree for this problem.b. How many machines should the company purchase, and what is the expected payoff?